MATH 2328 Spring 2018 EXAM 1 7. (15 points) In a study investigating the effect

Question

MATH 2328 Spring 2018 EXAM 1 7. (15 points) In a study investigating the effect of car speed on accident severity, 5000 reports of fatal aut acidents were examined. The ditriution of the speds is unimodal and ormnetial with the mean cz and the standard deviation 14 mph. Use the Empirical Rule to draw and clearly label this model show intervals and percentages) a b. What percent of accidents occurred with the speed between 28 and 42 mph? more than 70 mph? is more unusual: an accident with the speed 15 mph or 75 mph? Explain your reasoning statistically. Extra problem-10 points. No partial credits. Show all work. 78 and a sample variance s. 124.8 ,x, has a sample mean lue. It was missing when the list was formed. This value, A sample consisting of 10 values happens It is discovered that there is a 11th data va numerically equal to 78. a. What is the sample mean of the whole list of 11 values? Explain using formulas What is the sample variance of the whole list of 11 values? Explain using formulas.

Explanation / Answer

7.

Mean = 42

Stdev = 14

a.

b.

Answer to the question is as follows:

28 is 1 deviation below mean, and 0 is mean.

P(between 28 and 42) = P(-1<Z<0) = .34

- more than 70 mph

70 is 2 deviation more than mean.

So, the are more than 2 deviation above mean is .025 or 2.5%

c. Lets see, first calculate Z.

Z1 = (15-42)/14 ~ =-2

Z2 = (75-42)/14 = 33/14 = 2.35

So, more unusual is the event where Z is more is magnitude. 75mph is more unusual

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